We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons" at finite temperatures. This model describes a system of cold bosonic atoms with two species in an optical lattice. The model is derived from the Hubbard model for very large on-site repulsive interaction between bosons of same species (hard-core nature) and also strong correlations between different species. The operator B_{x��} for an atom at the site x with a two-component (pseudo-) spin ��(=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a spinon described by a CP^1 field (Schwinger boson) z_{x��} and a holon described by a hard-core-boson field ��_x as B_{x��}=��^���_x z_{x��}. ��_x is then expressed by a pseudo-spin, which is, in turn, represented by another CP^1 (pseudo) spinon w_{x��} as ��_x = w_{x2}^���w_{x1}. We then have a double-CP^1 representation of the model by z_{x��} and w_{x��}. By means of Monte Carlo simulations of this bosonic t-J model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. They should be compared with the possible experimental results of a recently studied boson-boson mixture like ^87Rb and ^41K in an optical lattice.

13 pages, 17 figures